Abstract
Scoring multipie-choice questions according to the simple scoring systems S1 = R, where R is the number of correct answers, produces an upward bias in scores of poorer students as a result of guessing. The scoring formula conventionally used to adjust for guessing is S2 R-W/(n-1), where W is the number of wrong answers and nis the number of choices per question. However, S2 is based on the unrealistic assumption that on each question the student either knows the correct answer or guesses randomly. On the basis of a more realistic assumption an alternative scoring formula is derived, S4 = [nR + (n-1)Q - Q2/R]/2(n-1), where Q is the number of questions. Compared to S4, the conventional formula (S2) has a downward bias for Q/n < R < Q and the simple formula (S1) has a downward bias for Q/(n-2)<R<Q in addition to its upward bias for R<Q/(n-2).
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